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let [root(n 2 +1)]=[root(n 2 +λ)] , where n, λ€N . show that λ can have 2n different values.

let [root(n2+1)]=[root(n2+λ)] , where n, λ€N . show that λ can have 2n different values.

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1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hello
Well for [root(n^2+1)] =n for any n greater than 0
n^2+lamda should between n^2 and (n+1)^2
=> (n+1)^2-n^2=2n+1 if we include 0
So it can have 2n+1 different values
take 2,3
9-4=5 which is 2*2+1 if we include 0
Thanks & Regards
Arun Kumar
Btech IIT delhi
Askiitians Faculty

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